Monday, November 3, 2008

The Babelian algorithms

If you are reading this blog, chances are you have read Jorges Luis Borges' Library of Babel, which opens its shelves unto the infinite:

The universe (which others call the Library) is composed of an indefinite and perhaps infinite number of hexagonal galleries, with vast air shafts between, surrounded by very low railings. From any of the hexagons one can see, interminably, the upper and lower floors. The distribution of the galleries is invariable. Twenty shelves, five long shelves per side, cover all the sides except two; their height, which is the distance from floor to ceiling, scarcely exceeds that of a normal bookcase. One of the free sides leads to a narrow hallway which opens onto another gallery, identical to the first and to all the rest. To the left and right of the hallway there are two very small closets. In the first, one may sleep standing up; in the other, satisfy one's fecal necessities. Also through here passes a spiral stairway, which sinks abysmally and soars upwards to remote distances. In the hallway there is a mirror which faithfully duplicates all appearances. Men usually infer from this mirror that the Library is not infinite (if it were, why this illusory duplication?); I prefer to dream that its polished surfaces represent and promise the infinite ... Light is provided by some spherical fruit which bear the name of lamps. There are two, transversally placed, in each hexagon. The light they emit is insufficient, incessant.

The idea of the story is persistently appropriated and repurposed, some even postulating a VHS version. But I suspect most take it as a given that the fantastic realm envisioned by this fiction is a logical impossibility, a metaphysical experiment that no earthly physic could realize, created by an author who viewed mathematics as a branch of fantastic literature. Now, an American math professor has released a tome which extrapolates the rules articulated into the story to provide an actual plan for the library. From Alberto Manguel's review in the New York Sun:

In 1939, employed in a small municipal library of Buenos Aires where the oafishness of his colleagues made him weep with daily frustration, the 40-year-old (and still largely unknown) Jorge Luis Borges collected a few of the reading notes he had made on the streetcar to and from work, and pieced together a short text which, under the title "The Total Library," he sent to the magazine Sur, where it appeared in the August issue. The essay, which links the names of Democritus, Lewis Carroll, Cicero, and the forgotten German fantasy writer Kurd Lasswitz, was developed a couple of years later into another, slightly longer one, "The Library of Babel," which Borges eventually included in his collection "The Garden of Forking Paths" (later expanded under the title of "Ficciones"). The end-paper pages of William Goldbloom Bloch's "The Unimaginable Mathematics of Borges' Library of Babel" (Oxford University Press, 192 pages, $19.95) reproduce the first and last pages of Borges's manuscript, showing that it was written (in what Borges called "the handwriting of a dwarf") on accounting sheets with the heading Haber, or "Credit," in Gothic letters that magically make the "H" look like a "B" and the "r" like an "l."

(I have always reveled in those images of Borges the branch librarian writing his ficciones on the streetcar, elucidating the mysterious epic wonder latent in the most mundande and tranquil everyday as the wheels slowly trundle through the leafy avenues. Perhaps an anachronism on my part, but I consider that commute to the fantastic the bookend to Che's motorcycle road trip.)

Manguel summarizes Bloch's approach to the problem:

In Borges's imagining, the Library of Babel itself is a building composed of an indefinite number of hexagonal galleries. A ventilation shaft in the center of each allows the visitor to see the floors above and below, in endless sequence. Each wall of each hexagon holds 32 books of identical size; each book has 410 pages; each page, 40 lines; each line, approximately 80 letters. All possible combinations of the 25 orthographic symbols make up the books; therefore, every conceivable book must exist in the monstrous library. In his story, Borges gives just a few examples of what might be found here: "the detailed history of the future, the autobiographies of the archangels, the faithful catalogue of the Library, thousands and thousands of false catalogues, the proof of the falsity of those false catalogues, the proof of the falsity of the true catalogue ..."

The numbers he chose for the shelves and books in his story, Borges later confessed, were simply those of the municipal library in which he worked — and which he himself found so horrible. "Learned critics," he noted later, with some evident pleasure, "studied these figures and generously lent them a mystical significance." Mr. Bloch, with similar generosity, and in an exercise he himself describes as "tedious, uninspired, but straightforward" if carried out in full, asks whether our entire universe could in fact contain this dizzying number of books. Even if it could (if the size of the library, as Borges suggests, coincided with that of the universe), the inconceivably vast space would make it impossible for a human librarian to even barely begin its exploration. Walking 60 miles a day for 100 years, notes Mr. Bloch, our vigorous librarian would only travel a distance slightly less than that which light covers in two minutes. "To cross our universe, which is incomprehensibly dwarfed by the Library, light would need to travel for a least 15 billion years." It would take a librarian, moving at the leisurely pace of a connoisseur, considerably longer — a mathematical certainty that mirrors the nightmarish vision Borges said he wished to convey.